Automatic rapid melting system and its application for arc furnace

ABSTRACT

An electric power supply program is set for controlling a steel making arc furnace. According to this program, a steel melting period is divided into a plurality of successive melting sections in each of which a predetermined total of electric power is to be supplied to the arc furnace at an optimum power level. The electric power which is actually consumed is integrated during each of said melting sections. Power level is switched from the optimum power level programed for one of said melting sections to that programed for the next section when the amount of electric power consumption actually integrated in said one melting section becomes equal to the predetermined total of electric power programed for said one melting section, thereby a melting electric power is supplied to the arc furnace at the optimum power level programed for said next melting section. A power factor program is also set. According to this power factor program, a melting electric power is to be supplied to the arc furnace with a predetermined power factor to provide an optimum length of arc for each of said melting sections. The power factor is maintained at the predetermined optimum value for each of said melting sections by controlling the current into the arc furnace by use of the deviation of the actual power factor from the power factor programed for the section. Moreover, the total electric power Y which is necessary in melting the charge of steel material is tentatively determined. First electric power Y1 which is consumed for each of a plurality of definite, ever increasing periods from the beginning of melting operation is determined and second electric power Y1 per unit time consumed just before the end of each of said definite periods is determined. The value X of remaining period of time which is expected to be taken before the termination of the melting operation is estimated from the following equation, X (y - Y1)/Y1, and the value of X is indicated at every estimation to inform the operator of the remaining period of time from the end of each of said definite periods to the termination of the melting operation.

United States Patent vTakanasi et al.

[54] AUTOMATIC RAPID MELTING SYSTEM AND ITS APPLICATION FOR ARC FURNACE1 [72] Inventors: Haruo Takanasi, Kasugai; Sadale Sone,

Kuwana; lsamu Eguchi, Nagoya, all of Japan Daldo Seiko'Kabushlkl Keisha,Minamiku, Nagoya-shi, Ai hi-ken, Japan 221 Filed: Mar. 17,1970 1211Appl.No.: 20,248

[73] Assignee:

[30] Foreign Application Priority Data FORElGN PATENTS OR APPLICATIONS18,835 8/1968 Japan. ..l3/12 135,986 5/1961 U.S.S.R.'........ ....l3/13901,365 6/1962 Great Britain ..l3/l2 959,715 6/1964 Great Britain..l3/12 Primary E.raminer--l-larold Broome Assistant Examiner-F. E. BellAttorney-Stevens, Davis, Miller & Mosher [451 May 2, 1972 [57] ABSTRACTAn electric power supply program is set for controlling a steel makingarc furnace. According to this program, a steel melting period isdivided into a plurality of successive melting sections in each of whicha predetermined total of electric power is to be supplied to the arcfurnace at an optimum power level. The electric power which is actuallyconsumed is integrated during each of said melting sections. Power levelis switched from the optimum power level programed for one of saidmelting sections to that programed for the next section when the amountof electric power consumption actually integrated in said one meltingsection becomes equal to the predetermined total of electric powerprogramed for said one melting section, thereby a melting electric poweris supplied to the arc furnace at the optimum power level program'ed forsaid next melting section. A power factor program is also set. Accordingto this power factor program, a melting electric power is to be suppliedto the arc furnace with a predetennined power factor to provide anoptimum length of are for each of said melting sections. The powerfactor is maintained at the predetermined optimum value for each of saidmelting sections by controlling the current into the arc furnace by useof the deviation of the actual power factor from the power factorprogramed for the section. Moreover, the total electric power Y which isnecessary in melting the charge of steel material is tentatively deter-I mined. First electric power Y, which is consumed for each of aplurality of definite, ever increasing periods from the beginning ofmelting operation is determined and second electric power Y, per unittime consumed just before the end of each of said definite periods isdetermined. The value X of remaining period of time which is expected tobe taken before the termination of the melting operation is estimatedfrom the following equation, X= (y Y )/Y and the value of X is indicatedat every estimation to inform the operator of the remaining period oftime from the end of each of said definite periods to the termination ofthe melting operation.

1 Claims, 9 Drawing Figures r SCRAP 9 KWHR/TON WEIGHT T T POWERPRESETTER Z Qb figg cowsumpnow PRESETTER fi i r REVlSER SELECTOR 1 4FURNACE 2\ VOLTAGE INPUT PowER VOLTAGE CURRENT INTEGRATOR TAP-CHANGER v7 PowER- FACTOR CURRENT DETECTOR ADJUSTOR O E -FACTOR POWER- FACTOR PRESETTER 'FlG.2

Patented May 2, 1972 3,660,583

- 5 Sheets-Sheet 1 i I 02 LLI I k o I O. i 5 l I 0 TI T2 T3 7 TIME {8SCRAP 9 I KWHR/ TON rLLE POWER PRESETTER gi t gags; CONSUMPTIONPRESETTER REVISER SELECTOR FURNACE V T INPUT POWER VOLTAGE I CURRENTINTEGRATOR TAP-CHANGER 7 POWER-FACTOR T CURRENT DETECTOR ADJUSTOR HARUOTAKANASI SADAIE SONE ISAMU EGUCHI INVENTORS Patented May 2, 1972 5SheetsSheet 2 STANDARD I I I l I l' AZOFEISEZQPmEDmZOQ mmiom TIME FlGjmSTANDARD POINT TIME VARIATION ZOFDE?! mom wD omm mm FlG.3b

Patented May 2, 1972 3,660,583

5 Sheets-Sheet 5 POWER CONSUMPTION(KW HR/TON) To 1" T2 T T3 ELAPSED TIMEFIG.5

Patented May 2, 1972 5 Sheets-Sheet 4 RON-LINE PRESETTER PROGRAMME powen LEVEL VOLTAGE'TAP PROGRAMME MODIFIER (I6 BASE VALUE PRESETTERAUTOMATIC DETECTOR -ROOF TEMP. -WALL TEMP.

OVER-CURRENT TRIP CURRENT FLUCTUATION PRESETTER I FlG.6

BASE VALUE PRESETTER COMPARISON DEVIC AUTOMATIC DETECTOR -POWERCONSUMPTION 'ELECTRODE CONSUMPTTON 'MELTING HOURS 5 Sheets-Sheet .J

Patented May 2, 1972 CALCULATOR FOR I 26 msu'me TIME I v 22 v BASE VALUEf PRESETTER STANDARD POWER r cousum nou MODIFIER PRESETTER KWHR/TONREVISED REVISER CURVE CHANGER DETECTOR -MELTING nouns BATH TEMP. F'G 7-MELT|NG ASPECT 32 POWER-FACTOR BASE VALUE CONTROL PRESETTER 29 I f soPOWER-FACTOR F COMPARISON PRESETTER Mom DEVICE DETECTOR ELECTRODE BROKENREFRACTORY ERROSION 'MELTING HOURS -POWER CONSUMPTION AUTOMATIC RAPIDMELTING SYSTEM AND ITS APPLICATION FOR ARC FURNACE BACKGROUND OF THEINVENTION Recently, as a control method of melting power for arefurnaces, BISRA (British Iron and Steel Research) has developed APIC(Automatic Power Input Control System). In this system, which isdisclosed in British Pat. No. 901,365, input power can fundamentally becontrolled only by two factors control of the consumption of meltingpower and control of the melting time. I

With its application to are furnaces, however, the results by meltingare always apt to have the different aspects because of a lack ofuniformity inthe size and physical characteristics of the materialsto'be supplied and also an instability of power input, both of whichwill be easily caused by the change of the power consumption and themelting time.

SUMMARY OF THE INVENTION The APIC-type control in the first meltingstage can be automatically attained through the final power-up to themaximum input (Ps) after necessary power inputs (P P which willpreviously be fixed, during the given time (T T as shown in the FIG. 1.

In the abovesaid control, one often has such unsuccessful encounterswith inefficient operation and low productivity with the result that themelting time elapsed (T T in the early melting stage is excessive orsometimes insufficient for optimum control mainly because the process ofmelting based on their average program will go on without any adjustmentto the change of both the charge material and power input condition.

And further, in the BISRA system, it is thought that it is satisfactoryif its value of input power consumption equals that of the product ofcharged material weight and the average input power for melting.

Under such a system, it is natural that inadequate control can be.attained as previously referred to in the preceding paragraph.

In consideration of such inefficiency, our system is devised toeliminate thesedefects in prior art systems.

BRIEF DESCRIPTION OF THE DRAWINGS A complete understanding of theinvention may be obtained from the following detailed description andexplanation which refer to the accompanying drawings illustrating thepresent preferred embodiment.

In the drawings:

FIG. 1 is a graph of input power level against elapsed time;

FIG. 2 is a block diagram of control system of our invention;

FIG. 3a shows a power consumption development against elapsed time, andFIG. 3b is a revised curve for power consumption;

FIG. 4 is a skeleton of control circuit for information of operationend;

FIG. 5 is the referring curves for information of end time, showingpower development against elapsed time;

FIG. 6 shows details of the power-factor-presetter and current adjusterof FIG. 2; and

FIG. 7 shows details of the-power consumption presetter and reviser ofFIG. 2.

The power-factor presetter 5 and current adjuster 7 are illustrated inFIG. 6.

As shown in FIG. 6, voltage and current signals from the main circuit ofan arc furnace are fed to a power-factor meter PF and thus an outputvoltage proportional to the power factor is taken out of thepower-factor meter PF. A power-factor presetter VR is connected across astabilized source of direct current E. This power-factor presetter VRsets a power-factor for each of the successive melting sections. Theoutput voltage from the power-factor presetter VR is proportional to itsset power-factor. As seen from FIG. 6, the power-factor presetter VRconsists of a first set of arelay contact S and a potentiometer VR,, asecond set of a relay contact S, and a potentiometer VR,, a third set ofa relay contact 5;, and a potentiometer VR etc., for the successivemelting sections, respectively. These relay contacts 8,, S 8,, etc., aresequentially switched on according to the amount of electric powerconsumption. During a melting section, the output voltage of thepower-factor meter PF is compared with the output voltage from the setof relay contacts and potentiometer corresponding to the meltingsection. If the output voltage of the powerfactor meter PF is greaterthan the output voltage from the power-factor presetter VR, a relay F 1is actuated to cause a current switch for the arc furnace to be drivenso that the current flow through the arc furnace may be increased toreduce the power factor. Conversely, if the output voltage of thepower-factor meter PF is lower than the output voltage from thepower-factor presetter VR, a relay F, is actuated to cause the currentswitch to be driven so that the current flow through the arc furnace maybe decreased to increase the power-factor. When the output voltage ofthe power-factor meter PF is equal to the output voltage from thepower-factor presetter VR, the present condition is maintained.

The comparison circuit comprising the relays F and F, and diodes may beprovided with an integrator A. The difference voltage between the outputvoltage of the power-factor meter PF and the output voltage from thepower-factor presetter VR is integrated by the integrator A for everyperiod as set in a timer T. An average value is obtained from theintegrated difference voltage for each period. Relay F and F is actuatedin response to the average value. This means that sampling control canbe effected at intervals of the time of period as set in the timer T.Thus, more stable control can be achieved in the arc furnace.

DESCRIPTION OF THE PREFERRED EMBODIMENT The values of the powerconsumption according to the scrap weight for each melting section arepreset on dial-type switches on the power consumption presetter" l, andthen compared with the number of pulses from "input power integrator 2at comparison device 3 which comprises counters and AND circuitelements. When both values become the same, the output from comparisondevice 3 is sent to the voltage tap-changer 4 and the power level ischanged to the value preset for the following step. In this processing,the better the conditions of scraps and supply voltage are, the shorterthe power steps are, resulting in the higher power feeding rate and thusthe productivity can be improved. On the contrary, when the conditionsare not good, the changing speed becomes lower, but the procession isheld at the level matched to the condition of the scraps and supplyvoltage.

. B. Power-F actor Control The experiment in the practical are furnacehas shown that the power-factor for the optimum operation is about 75percent in early melting stage, and about percent in the last.

In the method described in this invention, the optimum power-factor ispreset on dial-type switches or pin boards at power-factor presetter" 5and compared with the load powerfactor sent from power-factor detector 6during operation. Through the control of current adjustor" 7 based onthe deviation of the power-factor, i.e., arc length can be heldaccordingly to the melting stage. C. Determination of Melting End Thescrap weight and power consumption set on dial-type switches or pinboards in kwhr./ton presetter" 8 are multipled at total kwhr.calculator" 9, and compared at 3 with the value of power consumptionsent from 2, and then melting end is informed or following process isreplaced, when the power consumption reaches the preset value.

On the way, power consumption set in 8 is revised into the proper valueby reviser 10. In the reviser, modifying curves shown in FIG. 3b arecalculated from practice, based on the relation between standard powerconsumption and melting hours.

For example, when power consumption is off the standard curve, kwhr./tonis modified in response to the deviation based on the modifying curve inFIG. 3b.

At FIG. 3a, when the deviation turns up from the standard curve, powerconsumption becomes less than standard, and, conversely, when thedeviation turns down, power consumption will go on increasing.

Each power step is selected in the selector 11 based on the processionof melting.

The presetter l and reviser are illustrated in FIG. 7.

As shown in FIG. 7, voltage and current signals from the main circuit ofan arc furnace are fed to a wattmeter kwhr.

A pulse is produced from the wattmeter KWhr. in response to theconsumption of a predetermined amount of electric power. For example,one pulse per 1 kwhr. is generated. These pulses are supplied to a pulsecounter 10 C. Power-consumption presetters 1 PR, 2 PR, 3 PR, for themelting section set a predetermined amount of power consumption for thecorresponding melting section at which amount the melting is switchedfrom the corresponding melting section to the next melting section. Arelay V, caused to be energized by a voltage presetter 10 PR through astarting button ST so that a suitable one of the voltage taps of the arcfurnace transformer may be selected. When the count of the pulse counter10 C becomes equal to the predetermined amount of power consumption asset in the presetter 1 PR, the presetter 1 PR generates an outputsignal. This output signal is fed to a NOT element 1 NT. This causes theoutput of the NOT element 1 NT to go to zero and then the output of theAND element OAN comes to zero. Thus, the relay V, which has beenenergized is deenergized to release the selected tap. Simultaneously,said output signal from the presetter 1 PR is also fed to an AND element1 AN. Then, a voltage presetter 11 PR is energized and thus a relay V isenergized so that another suitable voltage tap may be selected. This isequivalent to saying that the voltage applied to the arc furnace iscorrespondingly changed from one level to another level.

When the count of the pulse counter 10 C becomes equal to thepredetermined amount of power consumption as set in the presetter 2 PR,the presetter 2 PR generates an output signal. This output signal is fedto a NOT element 2 NT. This causes the output of the NOT element 2 NT togo to zerio and then the output of the AND element 1 AN comes to zero.Thus, the relay V, which has been energized through the presetter 11 PRis deenergized to release said another voltage tap. Simultaneously, theoutput signal from the presetter 2 PR is also fed to an AND element 2AN. Then, a voltage presetter 12 PR is energized and thus a relay V isenergized so that a further suitable voltage tap may be selected. Inthis manner, the voltage applied to the arc furnace can be suitablychanged according to the amount of power consumption during meltingprocess.

The weight of the scrap loaded is set in a presetter 21 PR.

The amount of power consumption which is usually necessary to melt out ascrap of unit weight is set in a presetter 22 PR. A presetter 23 PRserves as a revising setter. During the melting process, the set valueof the presetter 23 PR is automatically modified by a motor M.

The pulse signal from the wattmeter kwhr. is fed to a counter 11 C. Whenthe count of the counter 11 C becomes equal to that corresponding to theweight of the scrap as set in the presetter 21 PR, an output signal isgenerated. This output signal is supplied to an AND element 11 AN. Thissignal also resets the counter 11 C. Then, the counter 11 C begins tocount the pulse signal from the wattmeter kwhr. Thus, whenever the countof the counter 1 1 C reaches the value set in the presetter 21 PR, anoutput signal is supplied to the and element 11 AN. The pulses suppliedto the AND element 11 AN are counted by a counter 12 C. When the countof the counter 12 C reaches the value set in the presetter 22 PR, asignal is sent to an AND element 12 AN. This pennits the output of thepresetter 21 PR to pass to a counter 13 C. Simultaneously, said signalfrom the presetter 22 PR is also fed to a NOT element 11 NT. Thisprevents the output signal of the presetter 21 PR from passing to thecounter 12 C. The counter 13 C counts the pulses from the AND element 12AN. When the count of the counter 13 C reaches the value set in thepresetter 23 PR, a signal is generated. This signal energizes a relay Eso that a signal representative of the termination of the meltingoperation may be produced. An alarming signal representative of thetennination of the melting operation may be generated by use of anycontact of the relay E. Alternatively, a source of power for the arcfurnace may be switched off by use of any contact of the relay E. Thesignal representative of the termination of the melting operation isused to reset the counter 13 C to be prepared for the next meltingoperation. Namely, assume that the weight of loaded scrap as set in thepresetter 21 PR is W,, the amount of power consumption necessary to meltout a scrap of unit weight as set in the presetter 22 PR is P,, and therevising value of said amount as set in the presetter 23 PR is P,. Whenthe total PT of pulses fed to the counter 11 C becomes equal to W, X (P,P,), the relay E is actuated so that a signal representative of thetermination of the melting operation may be generated.

D. Operation End Time Information In the electrical operation of priorart devices, the operator can guess the end time of the operation onlyby experience and then, after the end of one operation, followingoperation can the be prepared, thereby resulting in loweredproductivity.

In this invention to improve the above mentioned defect, the operator isalways informed of the end time during operation and then the operatorcan perfonn the preparation of the following operation, resulting inhigher productivity and more effective power utilization.

Referring now in detail to the drawing, FIG. 4, in the case ofpractically melting operation in the arc furnace, power consumption perscrap ton (kwhr./t) is based on experimental data. First, the powerconsumption Y kwhr./ton" is preset on the select switch lcs. Totalweight W ton of charged scrap is preset on the select switch 2cs. Totalpower required for melting is shown in the equation of Y X W, andmelting end will be determined when input power reaches to the value Y XW.

The detailed motion of the information circuit to which our invention isadapted, is as follows:

Pulse signal P, proportional to input power, for example, 1 pulse perkwhr., is put in counter 30 and then, as soon as pulse P, reaches theset value W on the select switch 20s, a pulse is put in counter 10 andcounter 3c is reset. After that, counter 30 counts pulse P, again. Asabove mentioned, whenever pulse P, reaches value W, one pulse is put incounter 1c. The counter 1c is counted as illustrativelyshown in FIG. 5,in which power consumption per ton (kwhr./ton) is graduated on thevertical axis and elapsed time on the horizontal axis. Now, the rate ofpower consumption in operation shown in line A, time T for value W seton the select switch 2cs, means the time required till the melting end.At time T,, on the way of the operation, power consumption is countedduring time t and the counted value y," means line B and means line C.The end time in case of line B is expressed in (T T,), in case of line Cin (T, T,). For example, the time (T T,) is calculated as follows:

If the t is one minute, (T T,) is expressed at (Y Y,) minute. Time T,T,) is expressed at (Y- Y,)/y, minute.

Referring to H6. 4, the above equation is illustrated as follows. Atfirst, switch SW excite time relay 1T. After 1 minute, contact Ta willclose and Tbwill open. Pulses from; select switch 20s are counted oncounter 40 through AND gate 2AN during 1 minute. When time relay IT isreset, counter 4c stops counting and indicate y,.

On the other hand, pulse sign P, of 30 500 l l-lz. generated by thepulse generator (not shown) put on counter 2c through AND gate SAN. Whenthe counts of the counter from output of counter 30 become the same asthe count of the counter 2c by pulse P,, for example at value Y AND gateSAN excites AND gate 6AN, and then pulse P, is counted at counter 5cthrough AND gate 6AN. When the counts of the counter 4c and Sc'becomeequal, output from AND gate 7AN is counted to the counter 60, and thecounter by the output of AND gate 7AN is reset.

Then, pulse P, is counted by the counter 5c again, and the abovesequence is repeated till the counts of the counter 2c become value Ypreset on the select switch 1G8 and its output excite relay X. By theaction of the relay X, the counter 2c, 50 and 6c stop to count pulse PThe value display on the de'catron L based on the counts of the counter50, means the information time to the end of the operation. The displayis held for a time limited by the time relay 3'1, and the counter 20,4e, 5e and 6c are reset, and the above sequence is repeated. i

As above mentioned, by means of the end information apparatus adding tothe arc furnace input power control system, operators can always knowthe end time of the melting operation, and the preparation for nextprocessionis smoothly arranged and the working efficiency is greatlyimproved.

E. Improvement of the Program As above mentioned, the control system towhich our invention may be applied, is mainlybased on the programcontrol. Then, it is desirable that the control program is improved foroptimum control by means of the modification of the various valuespreseton the control program and the function of the standard powerconsumption and melting time. The improvement of the program isaccomplished by the research of the optimum set value through learningthe practical operation.

. Referring to FIG. 1, for example, set power level P P are limited bythe conditions of the refractory life of the furnace roof, and wall,electrode broken, over-current trip, etc. On the other hand, it isdesirable that power level P, and P be set at higher value because ofthe advance of productivity and the low power consumption. Therefore,power level P and P are determined from the entire view of the furnaceconditions, but

usually are set in the value estimated from the past experimentation, sothat it is not sure to set in optimum value.

The improvement of the set value to optimum value will be carried out bythe accumulation and study of sufficient practical data to cover thevarious conditions of the charge, furnace, and supply voltage. Theeffects of furnace operation may change due to variation of programmedset values. It is, therefollows:

l. About set values of input power level, voltage taps and powerconsumption for early melting stage l Erosion, life and temperature ofroof refractories,

(2) Electrode broken troubles and their causes,

(3) Aspect of consumed top of each electrode,

(4) Tri s of main circuit breaker due to over current,

(5) Swing of arc current, (6) Local errosion of hearth refractories,

' 7 Rate of electrode borin and soon.

2. Also 8 ut setvalue of input power level, voltage taps and powerconsumption for melting later stage:

(1 Erosion, life and temperature of wall refractories,

(2) Electrode broken troubles and their causes,

(3) Trips of main circuit breakerdue to over current,

(4) Electrode consumption,

(5) Power consumption,

(6) Productivity, and so on.

3. About set values of power consumption for whole melting:

( 1) Melting aspects and bath temperature,

(2) Productivity, and so on. 4. About set value of power-factor fittingto melting process:

(1) Electrode broken troubles andtheir causes,

(2) Erosion, life and temperature of refractories,

( 3 Productivity,

(4) Power consumption, and so on.

It will be evident from the foregoing that our invention ischaracterized by numerous advantages. ln the first place, the arcfurnace may be operated at optimum input power level. In the secondplace, power consumption can be modified to a suitable value for meltingconditions. Third, arc length for melting can be controlled by means ofpower-factor control. Fourth, control program may be optimized throughset value improving system.

What is claimed is: r 1. A method of controlling a 'steelmaking arcfurnace including the steps of:

a. setting an electric power supply program according to which a steelmelting period is divided into a plurality of successive meltingsections, a predetermined total of electric power being supplied to thearc furnace at an oppower thereby being supplied to the are furnace atthe op timum power level programmed for said next melting section;

b. setting a power factor program according to which melting electricpower is to be supplied to the arc furnace with a predetermined powerfactor to provide an optimum length of are for each of said meltingsections; and maintaining the power factor at the predetermined optimumvalue for each of said melting sections by controlling the current intothe arc furnace as a function of the deviation of the actual powerfactor from the power factor programmed for the section; and

c. determining tentatively the total electric power Y which is necessaryin melting the charge of steel material; determining a first electricpower Y, which is consumed for each of a plurality of definite, everincreasing periods from the beginning of the melting operation;determining a second electric power Y per unit time consumed just beforethe end of each of said definite periods; estimating the value X of theremaining period of time which is expected to be taken before thetermination of the melting operation from the following equation,

X Y-Yl Y, and indicating at every estimation the value of X to informthe operator of the remaining period of time from the end of each ofsaid definite periods to the termination of the melting operation.

1. A method of controlling a steel making arc furnace including thesteps of: a. setting an electric power supply program according to whicha steel melting period is divided into a plurality of successive meltingsections, a predetermined total of electric power being supplied to thearc furnace at an optimum power level in each of said melting sections;integrating the electric power actually consumed during each of saidmelting sections; and switching power levels from the optimum powerlevel programmed for one of said melting sections to that programmed forthe next section when the amount of electric power consumption actuallyintegrated in said one melting section becomes equal to thepredetermined total of electric power programmed for said one meltingsection, melting electric power thereby being supplied to the arcfurnace at the optimum power level programmed for said next meltingsection; b. setting a power factor program according to which meltingelectric power is to be supplied to the arc furnace with a predeterminedpower factor to provide an optimum length of arc for each of saidmelting sections; and maintaining the power factor at the predeterminedoptimum value for each of said melting sections by controlling thecurrent into the arc furnace as a function of the deviation of theactual power factor from the power factor programmed for the section;and c. determining tentatively the total electric power Y which isnecessary in melting the charge of steel material; determining a firstelectric power Y1 which is consumed for each of a plurality of definite,ever increasing periods from the beginning of the melting operation;determining a second electric power Y1 per unit time consumed justbefore the end of each of said definite periods; estimating the value Xof the remaining period of time which is expected to be taken before thetermination of the melting operation from the following equation, X(Y-Y1)/Y1 ; and indicating at every estimation the value of X to informthe operator of the remaining period of time from the end of each ofsaid definite periods to the termination of the melting operation.